›
›

Tài liệu ôn thi THPT Quốc Gia môn Toán - Chuyên đề Hình phẳng oxy

pdf 32 trang Người đăng khoa-nguyen Lượt xem 944Lượt tải 0 Download
Bạn đang xem 20 trang mẫu của tài liệu "Tài liệu ôn thi THPT Quốc Gia môn Toán - Chuyên đề Hình phẳng oxy", để tải tài liệu gốc về máy bạn click vào nút DOWNLOAD ở trên
Tài liệu ôn thi THPT Quốc Gia môn Toán - Chuyên đề Hình phẳng oxy
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	 
0123432
	

	









 !"#$"%&%' ()*#"+ ,-").*/"+ )0"+



 5 
 !"# $%&$$'(")
    6 7 *+$'*,$$-   5  8=



 	

				 !	"	# $
	 5 %	 5  &  '(')	
*

 5

	+!	,
 -
 . /   0 15 − = − −

 % 02  . 35  =


 4 .  2 .5 − =

  //  / 15  =


.
. 5 
 !"# $%&$$'(")
    6 7 *+$'*,$#   5	  8=


. 	

		 5 		 !	"	# $
	 5 %	 5  &  '(')	

!
	 5 5	

	+!	,
 -
 2/  / 05 	 =

 %  / 0   0 .5 	− = −


 02   / /5 	 = − −

  02  . 35 	 =


/ 
/ 5 
 !"# $%&$$'("
)         ( ( 6 7 ( 6 7 
/ 	

		 5 		 !	"	# $ &
   ( 	+!	,
 -
 0 /   3 1 ( −  % . 1  . 6 ( 
 1 .  70 4 ( −    / 0  . 8 (− − 
0
0 5 1
$&(")  2   2 ( 8 
2$#$3$45*6  2 8 ≠ 
0 	

		 5  &   ( 	+!	,
 -
 . 2  2 1 (  % 70 2  2 8 ( − 
 2 3  7. 2 (   2 .  2 0 ( − 
7 	

		 5  & 9 '(9':	;	<=	+	(=	
	!$>	" : +	:	+!	,
 -
 ( )73/2   0(9 :∆ =  % ( )0/   3(9 :∆ = 
 ( )7. 70   .(9 :∆ =   ( )0 7/   3(9 :∆ = 
7 
7  5 
 !"# $%&$$'("
)   9 99 6 7 *+$'8'$9
: 	

		 5 	+!	,
 -
? & / 09 '($>$ .; = 
%? &  . 0 − '(	+':@ 
	;+(=	$ 31  
? & . 0( '(	+':	;+(=	$ 82  
; 	

		 5 	+!	,
 -
? &  1 69 − − '($>$ 0; = − 
%? & / . − '(	+':@ 
	;+(=	$ 82  
? &  / 0( − − '(	+':	;+(=	$ .2  
1
2
34<
www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
ww
w.
M
AT
HV
N.
co
m
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	 
01234<2
:
: 5 
 !"# $%&$$'(")
   9 6 7 *+11*6 - 26 (7 ∆ + + = 
=
*#3>$=	08
	>?@AB	0
C	0@DE
@F>*	0*	0>G
@AB	0
C	0
=AG!@AB	0
=	08H	
=	0
0!
H
I@E
=I	0
"
0!8
	

=	0H	8H		!H	
!H	J	K
!H	>	0!L
< 	

		 5  & 9 '(++':	 ∆ 	+!
	,
 A5-
 0 .  - 3 /2 / 29 6 7∆ − + =  %  / 4  -  0 29 7− − ∆ − = 

/ .
 1 .  -   
. 1
6 
9 
7 
 = − −
− ∆ ∈
= − +
  
00
1 0  - 
/ 0
76
9
−+∆ = ⋅
−

? 	

		 & 9 '(#	B	;	+=C+%D
 	+':	;	<==		!' EA	+!	,
 -
 ( )3/2 9 −  % ( )0/ 9 
 ( ). 0 9 − −   ( )0 / 9 − 

@ 	

	!	! ( %	D	 &!    (  ( 
FGF,	F(!&     9  
 H	<=	<	A   (∆ 	+!	,
 -
 ( ) ( ) ( )//   14   / 3 9  
 −  % ( ) ( ) ( )0/   1 .   . 3 9  
 − 
 ( ). /0  /  / 0 
0 0
9  

   
− − −   
   
  ( ). 4 0   .  / 3 
0 0
9  

   
   
   

:
: 5 
 !"# $%&$$'(")
   9 6 7 *+*A'$*6 - 26 (7 ∆ + + = 
=
*#3>$=	08
	>?@AB	0
C	0@DE
@F>>	00M>G
@AB	0
C	0
=AG!@AB	0!@AB	0
=	0
=N
=	0
0!
H
=N
"!
H
"8	;O	
@AB	0
=P		0+
QR
0!
HH	QSE
@F)	@AB	0!
H@F@6T	0S@F
D@AB	0!>Q
RAU	0
=H	@AB	0
C	0@6T	0>G@AB	0
C	0DE
@AB	0
C	0
=AG!
8
	
=	0H	
!H	J	K
!H	>	0!H	
	0>	0!L


 	

		 5  & 9 '(' E$':	 ∆  	+
!	,
 A5-
 3 /  - . 1 02/1 29 6 7− ∆ − + =  % 0 .  -  . 4 29 6 7− ∆ + − = 

.0
3 8  - 
. /2
76
9
−+
− ∆ = ⋅
−
 
0
/ 2  -   
/ 3
6 
9 
7 
 =
∆ ∈
= −
 

. 	

	!+     (( ′ ′ ′ '(		<=	I	A  	+ (∆ H
	A	J+	
 (∆ 	+!	,
 A5-
 - 0 . / 2  - . 4 2  - 1 0 / 2( 6 7 ( 6 7  6 7− − = + + = − + = 
% - 0 0 2   - 3 1 6 2  - 3 6 2( 6 7 ( 6 7  6 7+ + = + − = − − = 
 ( ) ( ) ( )7. 71   3 78   . /  (    ( ) ( ) ( )/ 0   1 0   / 7.  (  

/ H K& 9 FB	 5 '(& 9′ LM': 9  
	 5 	+!	,
 A5-
 ( )0/   - 0 . 29 5 6 7+ − =  % ( ). /   - 0 1 .2 29 5 6 7− + − = 
 ( )3/   - 0 3 29 5 6 7− + =   ( )1/.   - 0 . . 29 5 6 7− − − = 

0 NO


		 5′ LM':	 5  	 ∆  	+
!	,
 A5-
 - 0 / 2  - . 3 0 25 6 7 6 7− + = ∆ − + =  % - 0 3 2  - 0 0 25 6 7 6 7− + = ∆ + − = 
 - / 2  - . . 25 6 7 6 7+ − = ∆ − + =   - 0 . / 2  - 0 . / 25 6 7 6 7− + = ∆ − − = 
www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
ww
w.
M
A
HV
N.
co
m
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	 
01234V2
 !"56"789".'":)!$"+)+;()*#"+ ,-").*/"+()<"+

7 KP5	"Q+R!	S& 9 
	 ∆ 	+!	,
 -
 3 1  - . 3 6 29 6 7− ∆ − + =  % . 1  - / 29 6 7∆ + + = 

0
3 1  -   
0 .
6 
9 
7 
 =
− ∆ ∈
= +
  
/0
. 1  -
0 .
76
9
+−∆ = ⋅ 

: T+ (∆ P5	">	"	! ( 	+!	,
 -
 7/ 7/  0 73  3 . (   % 70/3  3 70  1 73 (  

; 	

		 5  &  '(! ( =	Q+R%D  +	:
	+!	,
 -
 7/ 0  . 1  . (  =  % 7/ .  3 0  1 (  = 
 1 /  0  7 .  1 (  =   . 2  2 3  3 (  = 

< 	

		 5 ++'(!	∆=	Q+R  	+!
	,
 A5-
 - 0 . 2 16 7 ∆ − + = =  % - . 2 17 ∆ − = = 
 - 0 2 36 ∆ − = =  
.
-   .
0 3
6 
7 
 =
∆ ∈ =
= +
 

? 	

		 5 ++':	 ∆ '(!  =	Q+R  
	+!	,
 A5-
 - . 3 /0 2 0 . 06 7  ∆ − + = =  % - 3 0 2  0 . .6 7  ∆ + − = − = 
 - . 2 . 1 17  ∆ − = − =   - 0 2 ./ 36  ∆ − = = 
.@ 	

		 5 !@ &    ( 	+!	,
 A5-
 0 1  7/ 0  1 39  (  % / 0  0 .  3 719  ( 
 /2 0  . 2  71 39  (   0 .  . 7/  . 19  ( 
.
 	 

 	  	 5     & 9  '( ! @   &    (  	+ !
	,
 A5-
 ( ) ( ) ( )0 1   7/ 0   1 3 9  (  % ( ) ( ) ( )/ 0   0 .   3 71 9  ( 
 ( ) ( ) ( )/2 0   . 2   71 3 9  (   ( ) ( ) ( )0 .   . 7/   . 1 9  ( 
.. 	

		 5 %	D 5 !&  =	Q+R%D  ! ( =	
Q+R%D ; 	+!	,
 -
 ( ) ( )/ /   0 .   0  3 (  ;= =  % ( ) ( )0 1   7/ 0   /  . (  ;= = 
./ H"$C!	 -
 / 0- 0 / 2 - . // 25 6 7 5 6 7− − = + − =  % / 0- 0 1 2 - . 8 25 6 7 5 6 7− + = + − = 
 / 0- . 4 08 2 - 0 1 /. 25 6 7 5 6 7− + = + − =   / 0- . 3 1 2 - 3 . // 25 6 7 5 6 7+ − = − + = 
.0 H"+!$	+	! ( 	+!	,
 -
 - 0 . 0/ 2 - 0 . U 2 - . 0 8 2( 6 7 ( 6 7  6 7− + = + + = − − = 
% - 3 . /0 2 - . 3 03 2 - . 3 8 2( 6 7 ( 6 7  6 7+ + = − − = + − = 
 ( ) ( ) ( )7. 71   3 78   . /  (    ( ) ( ) ( )/ 0   1 0   / 7.  (  
.7 T+   	 5  '( ∆  H   & $ C   	 $ %D α  	+ !
	,
 A5-
 ( ) ( ) ( ) 2- 0 . 3 / 2  - / 0 0 2  31 5 6  7   6  7 + − + − = ∆ − + + + − = α = 
% ( ) ( ) ( ) ( ) 2- . / . 2  - 0 / / 2  U2 5  6  7   6  7 + − − + − = ∆ − + + − − = α = 
.: 	

		 5  &  '(	+':	 ∆ =	$ α ':-
www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
ww
w.
M
AT
HV
N.
co
m
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	 
0123442
 ( ) 28 0  - . 0 8 2 31  6 7∆ + − = α =  % ( ) 202  - . . 2 31  6 7− ∆ + − = α = 
 ( ) 20 1  - . 8 2 82  6 7∆ + + = α =   ( ) 2/ .  - 2 .2  6 7∆ − = α = 
.; 	

	!
A!!$	+%V	 / 0 5 5 +	:
	+!	,
 A5-
 / 0- . 3 /0 2 - /0 1 02 25 6 7 5 6 7− + = + − =  % / 0- . 3 U 2 - 6 8 / 25 6 7 5 6 7− − = − + = 
 / 0- . 8 2 - . 0 25 6 7 5 6 7+ − = + + =   / 0- 0 // 2 - . 8 1 25 6 7 5 6 7+ − = − − = 
.< T+ (∆ P5		A'(%!Q"	J=	
 (∆ 	+!	,
 -
 - 0 . 0/ 2 - 0 . U 2 - . 0 8 2( 6 7 ( 6 7  6 7− + = + + = − − = 
% - 3 . /0 2 - . 3 03 2 - . 3 8 2( 6 7 ( 6 7  6 7+ + = − − = + − = 
 ( ) ( ) ( )7. 71   3 78   . /  (    ( ) ( ) ( )/ 0   1 0   / 7.  (  
 !"%&%' ()*#"+ ,-").*/"+ ,="#$"
.? 	

		J   $	A  '( &  	+!	,
 -
 ( ) ( )0 3   7/ .    % ( ) ( )7. 0   / 7/   
 ( ) ( ). 1   4 0     ( ) ( )22   3 3   
W ( ) ( )7/ 2   . 7//    X ( ) ( )/ 0   1 0   
/@ 	

		J   $	A  '(	
LY':	 ∆ +	:	+
!	,
 A5-
 ( ). 3  - 3 . /1 2 6 7∆ − + =  % ( )0 .  - 1 /0 4 2 6 7∆ − − = 
 ( ). 0   6− ∆ ≡   ( ). 1   7− − ∆ ≡ 
W ( )/ 0   - 0 4 2 6 7− ∆ − + =  X ( )22   - 0 2 7 6∆ − = 
/
 	

		J   $Q" ( 	+!	,
 A5-
 ( ) ( )70 .   8 1  (  % ( ) ( )2 /   1 /   
 ( ) ( )7. 3   4 0  (   ( ) ( )1 0   . 8  ( 
W ( ) ( )/ /   4 1  (  X ( ) ( )/ 1   / /  ( − 
/. 	

		J    &   ( '($	A  D	B	
∆ 	+!	,
 A5-
 ( ) ( )0 .  //  - . // 2 ( 6 7− ∆ − − =  % ( ) ( )2 3  0 8  - 0 1 2 ( 6 7∆ − + = 
 ( ) ( )0 0  68  - 1 . 8 2 ( 6 7∆ − + =   ( ) ( )/2   / 0   - / 2 ( 6 7− ∆ − − = 
W ( ) ( )/ 0   .2   - 4 8 2 ( 6 7− ∆ + − =  X ( ) ( )22   / 0   - 2 ( 6 7∆ − = 
// 	 

 	  	J        &   (  '( 	
 LY ':  	 ∆ 
	+!	,
 A5-
 ( ) ( )/ 0  . 3  - . . 2 ( 6 7∆ + − =  % ( ) ( )8 .  . 0  - 0 0 2 ( 6 7∆ + − = 
 ( ) ( )/ 0  0/  - 0 0 2 ( 6 7− − ∆ − + =   ( ) ( )02  3 0   ( 7∆ ≡ 
/0 	

		J    &  	
LY':	 ∆ 	 ( 	+
!	,
 A5-
 ( ) ( )08  - . 3 /1 / .  6 7 (− ∆ − = −  % ( ) ( )0/  - . 0 8 3 .  6 7 (− ∆ − = 
 ( ) ( )8 0   82  6 (− ∆ ≡   ( ) ( )3 .  - 0 . 2 .2  6 7 (− ∆ + − = 
/7 	

		J &Z'(	
LY':	∆/'(∆0':
 ( )0 .   / - . 3 / 26 7∆ − + =  0 - 3 . 4 26 7∆ + − = 
www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
ww
w.
M
AT
HV
N.
co
m
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	 
012342
% ( )/ .   / - 0 0 26 7∆ + + =  0 - 0 U 26 7∆ − + = 
 ( )22  ≡  / - 3 26 7∆ + − =  0 - 3 26 7∆ + + = 
 ( ). 8  −  / 6∆ ≡  0 7∆ ≡ 
/: 	

		J	
LY':	∆/∆0'($	AD	B
	':
 / - . 0 . 26 7∆ + + =  0 - 0 . /1 26 7∆ − + =  - 25 6 7− = 
% / - 3 26 7∆ + + =  0 - 4 3 26 7∆ − + =  - 3 . 0 25 6 7+ − = 
 / - 3 . /8 26 7∆ − − =  0 - . 3 . 26 7∆ + + =  - 0 . 25 6 7− + = 
 / - 3 0 26 7∆ + − =  0 - 3 /4 26 7∆ + + =  - 1 25 6 7− + = 
/; 	

		J+	
	!Z[T':
 ( ) ( ) ( )0 2   2 7.   1 7. (   % ( ) ( ) ( )1 .   8 0   . 7/ (  
 ( ) ( ) ( )/ 0   . /   7. 7/ (    ( ) ( ) ( )7/ 74   73 7.   2 2 (  ≡ 
/< 	

		J=	
	!Z[T':
 ( ) ( ) ( )0 8   7. 73   1 2 (   % ( ) ( ) ( )0 2   2 7.   1 7. (  
/? NO


		J ( ) LM':  ′  	 -5 
 ( ) ( ) ( )0 0\ - / 0 3 6 7− + − =  - / 25 6 7− − = 
% ( ) ( ) ( )0 0\ - 0 . . 6 7− + − =  - / 25 6 7+ − = 
 ( ) 0 0\ - 0 3 . 2 6 7 6 7+ − − + =  - 0 25 6 − = 

 !"56"789".'">5(#$"
0@ T+WF
  W ]!^=(!	;	B I	+=!	B &	+=!*	A


	! _  W ':  W $

	-
 ( ) 00- /
U 3
76
W + =  % ( ) 00- /
3 /
76
W + = 
 ( ) 0 0- /8 01 322W 6 7+ =   ( ) 0 0- 3 /W 6 7+ = 
W ( ) 0 0- U /8 /33W 6 7+ =  X ( ) 0 0- 8 U 13W 6 6+ = 
0
 NO


	"	#WF
	+!	,
 A5-
?=(	;F:%D8	;`%D3 %?=(	;F:%D/2	B I%D8
a=		B & //2X '(=(	;F: 0=  HB & / .2X − '( 
.
/
0
9
 
⋅ 
 
 

Wb &- ( ) ./ 2  /
0
9 
 
⋅ 
 
 
 X ( ) ( )3 .  0 0 . 9 − 
HB & ( )/ 62X − '(	A%D 31 ⋅  H;` 8=  _ 4 /86 = ± 
? & 6/09 '($%!Q" 	B &%B	!a%D02
c? & . 0 .9 '($%!Q" 	B &%B	!a%D 3 . 
QT$

	!CO	
VF( U  .6 7= ± = ± 
F? &
. 3

1 1
9
 
 
 
'( / 09X X∆ ' E	a
KCO	
V  W $=	D	B	 - 0 25 6 − = '($=(
)+%D8
www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
ww
w.
M
AT
HV
N.
co
m
	

		 
 !"		!"	
#$%&''&'%%


()	*+	$*,)-.	/	 
012342
T$*F( / 12 − '(

		J+	
CO	
V$F(
0 0  - .3 6 7+ = 
+T$*F( /28( '(

		J+	
CO	
V$F(
0 0  - 8/ 6 7+ = 

 T$=(	;F:%D 3 0  !*	B	;`'(!	B &  W 9D
	B=		J
0. HC&	BWF
 ( ) 00- /
/8 4
76
W + = $%!Q" 	B &%D
1
0
⋅ 
0/ HC&a	BWF
 ( ) 00- /
01 U
76
W + = ++> 0%!Q" 	B &
.0
1
= ⋅ 
00 T+WF"
 ( ) 00- /
01 3
76
W + = HC&aD	B  W +++/ 0X 9X F(
 U2   % /02    .2  
07 HC&  9 W∈ 	B &:/$ 2 2 2 2.2  31  82  /02  
 0 0  - U 01 001W 6 7+ =  % 0 0  - U /8 /33W 6 7+ =   0 0  - 4 /8 //0W 6 7+ = 
0: T+WF
 0 0  - U UW 6 7+ = H  9 W∈ ++-
 / 00 9X 9X=  % / 0. 9X 9X=  
/ 0 / 0
/ / 8
9X 9X X X
+ = ⋅ 
 !" -?.@?% !"A ,B#$" ,!"+)-"))C()0"+DE
0; H+d	
':>	;	<= 67 +%&- ( ) ( ) ( )/2   . 1   2 .  ( − − 
TM     (  F(%*=		!'(	" + ( 
%H	<& 9 ++- 0 . 29 9( 9+ − =
   

H	<=& X ++ 1X X= = 
H	<=&  ++ ( F(%(
WH	O
,
&& 
 ++- ( )0 . 
 
( 
 
( 
+ − = −     
0< H+d	
 67 +&  . 0  // (− H& 9 	B	;	 ++-
e>	" 9(∆ %D. % 0 0
 9 9(= + 	!	^`f	
?!
-
/
 2
3
 9
 
− 
 
+d
//
2
.
9
 
⋅ 
 

.
 2
0
8 9
 
⋅ 
 

0? H+d	
 67 +& / /  . 0 (− H& 9 	B	;	 ++-
g$ 31 9( =  %
4
  
09(
: @>5
∆ = 
?!
- ( ) 2 3 9 − +d ( )28 9  ( ) 2/8 9 +d ( )2 8 9 − 
7@ H+ d	 
 67  + & ( )0/   KP5 	 &  ( 6  7∈ ∈  + + (∆ 
' E	  '($>	"`f	h
?!
- ( ) ( )02   2/ (  
7
 H+d	
 67 + (∆ $	<	A ( ) ( )2 3   0 3   − − [		 & 9 
( D	B	 - 0 26 7∆ + − = H& 9 &=(+ ( #f	h
?!
-
/. 0/

3 3
9
 
− ⋅ 
 

www.MATHVN.com - Toán Học Việt Nam
 www.DeThiThuDaiHoc.com
ww
w.
M
AT

Tài liệu đính kèm:

  • pdfbai_tap_hinh_hoc_phang_Oxy_hay.pdf